
\section{Panbiogeography}

Panbiogeography is a unique and very useful approach to capture any
distributional pattern/structure in studies that use geographical data. Mapping
biogeographic tracks is a cost efficient way to reduce the initial complexity
that we find in the data sets \citep{Craw1989a}, as Croizat's tracks analysis
\citep{croizat1952, Croizat1958} provides a conceptual
framework for understanding the biogeographic structure and the relationships of
areas.

\index{Croizat:books}
Panbiogeography was developed by Croizat in his books, ''Manual of
phytogeography''\citep{croizat1952}, ''Panbiogeography''\citep{Croizat1958} and
''Space, Time, Form: The Biological Synthesis''\citep{Croizat1964}.
Panbiogeography was inspired by Croizat's idea of connecting two essential
elements in evolution: Space and Time: Earth and Life evolve together, which
means that biotas evolve together with the geographic barriers
\citep{MorroneCrisci1995, Morrone2000}.

Croizat's panbiogeography constituted a unique critique to Darwin's biogeography
ideas about natural selection, means of dispersal and geographic distribution
\citep{Craw1987}. This approach challenged the idea that means of
dispersal are the principal factors responsible for the evolution of the
distribution \citep{Craw1989b, Crawetal1999}.

Panbiogeography assumes that taxa distribution evolves through two stages:
mobilism and immobilism. The interaction of these two states is called vicariant
form-making model. Within the mobilism stage, an ancestor taxon expands to
establish on new territory through its means of dispersal (''means of
survival'') when the geographic and climatic factors are favorable. Later, when
the range geographic is established (immobilism) the appearance of barriers
allows the isolation and differentiation of taxa (vicariant form-making)
\citep{Grehan1988a, Michaux1989,  Crawetal1999, CrisciMorrone1992a}.

Panbiogeography has been considered an independent research program because is
the only approach that focuses on the spatial or geographical sector as a
fundamental pre-condition to any analysis of the patterns and processes of
evolutionary change \citep{Crawetal1999, Grehan1994, Grehan2001a}.

The assumptions that make the Panbiogeography different from other historical
biogeography approaches are \citep[][:19]{Crawetal1999}:
\index{Panbiogeography:assumptions}
''1. Distribution patterns constitute an empirical databases for biogeographical
analysis.

2. Distribution patterns provide information about where, when, and how animals
ans plants evolve;

3. The spatial and temporal component of these distribution patterns can be
graphically represented;

4. Testable hypothesis about historical relationship between the evolution of
distributions and Earth history can be derived from geographic correlations
between distribution graphs as geological/geomorphic features.''




\subsection{Track analysis}


Panbiogeography as a biogeographic method is called track analysis. There
are four principal concepts within this method: track, node, main massing, and
baseline \citep{CrisciMorrone1992a, Crawetal1999, Grehan2001a,
Espinosaetal2002}.
\index{Track analysis}
\index{Track analysis:individual tracks}

Individual tracks are the basic units of panbiogeography. These are lines drawn
on a map that connect different localities or distribution points of a
particular taxon or group of taxa, so that the sum of the segment lengths that
connect all the distribution points is the smallest possible. In the graph
theory words, the individual track is a minimum spanning tree
\citep{Crawetal1999, Morrone2004c, Page1987}.


\index{Track analysis:generalized tracks}
Generalized tracks or standard tracks are called repetitive patterns because
summarized distributions of diverse individual taxa \citep{Michaux1989}. These
are lines on a map resulting from the superimposition of the individual tracks.
Generalized tracks are interpreted as distributional patterns of ancestral biota
that had been fragmented by tectonic and climatic events \citep{Craw1988}. These
panbiogeographic element is considered as a conjecture (=hypothesis) of a common biogeography
history or primary biogeography homology sensu  \citet{Morrone2001a}, which means
that analyzed taxa are spatio-temporally integrated in a biota \citep{Craw1983a,
Morrone2001a, Morrone2004c}.
\index{Track analysis:nodes}

Nodes are areas or localities where two or more generalized tracks are
overlapped. These are complex areas or tectonic and biotic convergence zones
\citep{Craw1988b, CrisciMorrone1992a, Morrone2004c, Page1987}. The nodes are
considered priority areas for conservation or sites of biological endemism
because represented localities of high diversity, distribution boundaries,
disjunction, incongruence and recombination, specimens that are difficult to
identify and unusual hybrids \citep{Crawetal1999, MorroneEspinosa1998,
Grehan1993}.


The Panbiogeographic method involves basically main three steps
\citep{Morrone2004c}: Firstly, construction of two or more taxon individual
tracks (minimum spanning tree from distributional localities). Secondly,
delimitation of generalized tracks through geographic congruence between
individual tracks. Finally, determination of nodes within the intersection areas
between generalized tracks.

There are different approaches within panbiogeographic method. Croizat`s manual
reconstruction \citep{Croizat1958, Croizat1964}, Page's Spanning graphs
\citep{Page1987}, Craw's Track compatibility \citep{Craw1989a} and PAE
(''Parsimony Analysis of Endemicity'') \citep{Rosen1984, Crawetal1999,
Luna-vegaetal2000, MorroneMarquez2001}
\index{PAE}

\index{Track analysis:manual reconstruction}


\subsection{Croizat's manual reconstruction}

Croizat's manual reconstruction is done by drawing on a map taxon's individual
tracks and then overlapping them to determinate generalized tracks. Basically
the method consists of the following steps \citep{Morrone2004c}:

1. Connect the disjunct areas of distribution by lines forming individual tracks,

2. The individual tracks are oriented using baselines,

3. Overlap individual tracks to determinate generalized tracks,

4. Recognize the nodes where two or more generalized tracks are intersected,

5. Indicate on a map the generalized tracks,baselines and nodes.


\subsection{Page's Spanning graphs}

Page's Spanning graphs was the first attempt to quantify the panbiogeographic
analysis using graph theory. Its main methodological steps are \citep{Page1987}:
\index{Page's Spanning graphs}

1. connect the disjunct areas of distribution through a MST (Minimum Spanning
Trees) forming an individual track for each species,

2. Construct incidence and connectivity
matrices for individual tracks to recognized shared elements and track
congruence,

3. Construct a connectivity matrix for all tracks together to search
circuits that indicate incongruence tracks,

4. Indicate on a map the generalized
tracks, baselines and nodes.

\subsection{Craw's tracks compatibility analysis}
\index{Craw's tracks compatibility analysis}

Craw's tracks compatibility analysis \citep{Craw1989a} involves finding the
largest clique of compatible tracks through a locality/distribution per track
matrix \citep{Crawetal1999}. In general, its algorithm involves the following
steps \citep{Craw1989a, Grehan2001c, Morrone2004c}:

1. Construct individual tracks for different taxa from distribution localities using a MST,

2. Generate a matrix  (areas x individual tracks), where the presence of an area is
represented by ''1'' and its absence by ''0''.

3. Find the largest clique for compatible individual tracks which is considered the generalized track.

4. Evaluate statistically the generalized track,

5. Indicate on a map the
generalized tracks, baselines, and nodes.


\subsection{Parsimony Analysis of Endemicity}

\index{PAE:algorithm}

PAE (''Parsimony Analysis of Endemicity'') has been considered a
panbiogeographic method \citep{Crawetal1999, Luna-vegaetal2000,
MorroneMarquez2001, Morrone2004c}. Its algorithm includes the following steps
\citep {Morrone2004c}:

1. Construct individual tracks for different taxa from distribution localities using a MST,

2. Generate a matrix  (areas x individual tracks), where the presence of a species is represented by ''1'' and the absence by ''0''. Within this step, an extra area is added with ''0'' (all species absence) to polarize the topology (incorrectly called an 'area cladogram' \citep{pae2008}),

3. Analyze the matrix using a parsimony algorithm. Each clade supported by at least two individual tracks (as ''synapomorphies'') is considered a generalized track,

4. ''Disconnect'' or delete the species that support the different clades and reanalyze the matrix to search clades that are supported by other taxa \citep{Garcia-Barros2002},

5. Indicate on a map the generalized tracks, baselines and nodes.

Since \citet{Croizat1958, Croizat1964} presented his panbiogeographic method,
the above mentioned quantitative techniques had been proposed, Page's graph
theory method \citep{Page1987},
Henderson's analysis \citep{Henderson1989}, which is similar to Page's analysis,
and Craw's compatibility track analysis \citep{Craw1989a}. These techniques have
emerged taking
into account Croizat's framework for analysis: individual tracks congruence to
define generalized tracks \citep{Page1987, Henderson1989, Craw1989b}.
\citet{Page1987} suggested a quantitative approach using graph theory by
incidence and connectivity matrices, but this method has not been applied to
real data, perhaps because of its difficult calculation and computational
complexity. \citet{Craw1989a} proposed the compatibility track analysis based on
distributional compatibility which is analogous with Meacham's character
compatibility approach \citep{Meacham1984} to phylogenetic systematics
\citep{Crawetal1999}. Within the latter method, two or more individual tracks
are considered compatible if either one is included within or replicated by the
other. \citet{MorroneCrisci1995} claimed that the compatibility in
Panbiogeography is used in a restricted way depending on the method.
''Non-overlapping tracks'' are incompatible according to compatibility track
analysis and should be compatible in Croizat's track analysis by geographic
proximity.

Within the quantitative techniques proposed in the history of the
panbiogeography \citep{Page1987, Craw1989a, Henderson1989}, only
Craw`s compatibility tracks analysis has been implemented and now part of the
algorithm, the minimal spanning tree, has been automated in the software
package ''Croizat'' \citep{Cavalcanti2009b}.

Grid analysis such as PAE (Parsimony Analysis of Endemicity) has been
considered a panbiogeographic approach \citep{Crawetal1999, Luna-vegaetal2000,
MorroneMarquez2001, Morrone2004c}, but some authors do not consider it a
historical biogeography method \citep{Humphries2000, Garcia-Barros2002, pae2008}.
Although this method has been widely used \citep{Luna-vegaetal2000,
MorroneMarquez2001, Huidobroetal2006, Mihocetal2006, Espinosa-Perezetal2009,
Contreras-Medinaetal2007}, its implementation to the panbiogeographic analysis
was secondary. Its direct objective is the analysis of endemism and its relation
to the track analysis sensu Croizat could become ambiguous.

Despite of these methods, Croizat's manual reconstruction has been the most used
in panbiogeographic studies because its simplicity and the alleged direct
connection to Croizat's panbiogeographic concept. Nevertheless, the debate about
the reliability of the manual reconstruction is still
valid. The method turns to be ambiguous and generates subjective results with
large data set due to overcrowded points \citep{Franco-Rosselli2001, Liria2008}.



\section{Suggested literature}

\begin{itemize}
\item \citet{Crawetal1999} is a good summary of theories and methods, while the
empirical approach could be flawed.

\item \citet{Crisci2001} is an historical account of biogeography, and is
illustrative of the so called forces that shaped present biogeographic thought.
\end{itemize}
